On modified circular units and annihilation of real classes

TL;DR

This paper introduces a functorial method to study special p-units in totally real abelian fields, proving Solomon's conjecture on p-class group annihilation and deriving related results.

Contribution

It provides a new functorial approach to p-units that confirms Solomon's conjecture and extends understanding of class group annihilation in totally real fields.

Findings

Proof of Solomon's conjecture on p-class group annihilation.

New index formulae relating p-units and class groups.

Enhanced understanding of Euler systems in totally real fields.

Abstract

For an abelian totally real number field $F$ and an odd prime number $p$ which splits totally in $F$, we present a functorial approach to special "$p$-units" previously built by D. Solomon using "wild" Euler systems. This allows us to prove a conjecture of Solomon on the annihilation of the $p$-class group of $F$ (in the particular context here), as well as related annihilation results and index formulae.